Surface objective analyses (O3,PM2.5,NO2) for data assimilation

Alain Robichaud/ Richard Ménard

ARQI: air quality research division(Division de la recherche en qualité de l’air)

Outline

Objectives Theory, methodology Project OA (ARQI/AQMAS/CMDA) Applications and derived products Plans for 2012-2013

Overall objectives: • Develop a regional chemical data assimilation • Align the chemical data effort with the main stream meteorological data assimilation effort while adapting to the particularitiesof chemical fields in order to produce the best chemical analysis/forecast

OA is only a first step – not the ultimate goal

The main stream meteorological data assimilation system is based on• representations of errors by covariances • Hybrid EnKF-VAR for 3D regional/global• For surface assimilation: CALDAS

Purposes and applications of OA

Objective analysis using optimal interpolation is an essential first step in building up an assimilation system (such as EnKF). Producing maps of objective analysis (OA) on a regular basis is motivated by many factors such as:

1) to initialize numerical models at regular time interval (usually every 6 or 12 hours), i.e data assimilation

2) nowcasting purposes (AQ real-time forecasting) 3) help to trace back possible model bugs (or bugs in the

observation system) 4) produce long series of re-analyses for specific purposes (i.e.

climatology), study of trends which are more robust (no missing data in OA due to the intelligent spatio-temporal interpolator)

5) potentially useful for mapping health indices (AQHI), or specialized environmental indices or pollutant loadings on ecosystems,

Theory

OA is a problem of statistical optimization: minimizing the analysis error variance

Xa = (1-K)Xb + Kyo   (scalar form)   rearranging and introducing H (interpolation required)

Xa = Xb + K(yo –HXb) with K = (HPf)t * (H(HPf)t+R)-1 

(same equation as seq EnKF)                                             where

Xa: objective analysis field matrix ( dimension grid model) Xb: trial field (forecast or first guess from model) K : gain matrix (weight matrix)  ( dimension grid model X NS) yo: observation vector (dimension NSX1). H: interpolation operator for model at the station location (cubic semi-Lagrangian or linear).

Resolution 15 km grid (GEM-MACH), 21 km (CHRONOS)

Ozone objective Analysis : Current formulation

• OI type analysis solver

L

kxjixkkji

L

kxkxkkkk

where

BBT

BBT

TT

)(),(exp)(),,()(

)()(exp)()(),(

][)(

111

212121

1

HB

H(HB)

RH(HB)HBK

where (local parameters) estimated by local fitting of O-F on 3-hours intervals (from previous year data sets )and are global parameters estimated online by a method of maximum likelihood and chi2 adjustment

)(),( 21 kk BB

LB ,

particularities- some local and temporal variability of the error statistics (but based on previous year-hourly innovation statistics) has been accounted- online estimation (current analysis) of correlation length-scale and and global adjustment factor for representativeness error

Getting error statsFOAR modeling: covariance of OmP vs distance

Hollinsgworth and Lönnberg, 1986 (H-L)

Lci

…

Assumptions: 1) follow exp decreasing function 2) width of bins is fixed

3) cutoff distance 900 kms

Backgrounderror

- direct inversion (by Cholesky decomposition) of the innovation matrix and thus limited to ~1500 obs but we plan for next year to perform batch processing and eventually by SVD of innovations in an EnKF - statistical estimation of obs and background error variance – a time consuming process that often requires manual intervention. This procedure will be partially replaced by an online estimation of error variances using a combination of Desrozier’s and maximum likehood approaches- Non gaussian distribution of errors – relevant for aerosols. We plan to use the modified lognormal distribution (three paramaters – not two !!) as shown by daSilva (GMAO)

Drawbacks

For aerosols • Accounting for error of representativeness is fundamental• Non-Gaussian errors • Attribution of increments to primary or secondary aerosols is still not not well known

daSilva, 2010 - GMAO

MODIS

Project OA

Transfer to operations: objective analysis of surface ozone and PM2.5

D. Anselmo et P.A.Beaulieu (AQMAS) G. Verner, L. Veillette, Y. Zaitseva, I. Provost

(CMDA) ARQI (A. Robichaud,R. Ménard)

Monthly stats OA (from Yulia’s web page)

J U L Y

OCT

Ozone PM2.5

GEM-MACH oper 15 km

Applications

1) Data assimilation (surface AQ) 2) Diagnosing biases and model errors 3) AQHI mapping 4) Building climatology (O3 and PM2.5)

5) Others (oil sand monitoring, deep stratospheric intrusions to SFC, etc.)

Impact of data assimilation on AQ forecast

Std Dev O-P

Mean O-P

gain

F-testT-test

Impact of data assimilation on AQ forecast

Std Dev O-P

Mean O-P

Impact of data assimilation on AQ forecast

Mean O-P

Std Dev O-P

Existing product AQHI at stations20110815 at 18Z

Formula from Stieb et al. 2008 JAWMA AQHI=(10/10.4)*(100*(exp(0.00087*NO2)-1+exp(0.000537*ozone)-1+exp(0.000487*PM25)-1))

Model output of AQHIvs AQHI at the station

AQHI at the station

Proposed productAQHI map using OA

(OA of AQHI and AQHI calculated at the station)

A surface ozone and PM2.5 climatology (using an improved optimal interpolation scheme)

Presented at the 94th Canadian Chemistry Conference and Exhibition

Montreal, June 5-9, 2011

Presenter: Alain Robichaud

Collaborator/advisor: Richard Ménard

Comparison of sfc climatology with model outputs

CHRONOS ANNUAL AVG 2005

CHRONOS + AIRNOW SFC DATA AVG 2005

MOZART ANNUAL AVG

GEM-AQ ANNUAL AVG 2005

PM2.5 climatology

Randall et al(2001-2006)Satellite derived

CHRONOS+AIRNOW2004-2009

Remarks about this objective analysis

OA system presented here: Is not just mapping of ambient conditions It is also a tool for environmental monitoring,

input for data assimilation, tool for diagnosing model’s error & bugs, input for derived products (AQHI mapping, climatology, etc).

Plans for 2012-2013 fiscal year

Implementation plans• Operational implementation of regional surface ozone and PM2.5 hourly analyses should be completed by June 2012• Make recommendations for operational plans on chemical forecast. (chemical imbalance, primary vs secondary aerosols, better QC, code on-line or not, etc)• Introduce a change of variable for non-gaussian distribution of errors• Update the analysis solver to handle larger data volume of observations• Test the online methodology of obs and background error variances (Desrozier’s method combined with maximum likelihood estimation of correlation length-scales)

Scientific plans• Submit paper on OA with online maximum likelihood estimation of global parameters• Submit paper on implementation of CMC error covariances in BASCOE• Formal comparison between 4D-Var and EnKF of BASCOE•Submit paper on climatology and trend (10 year: 2002-2011)

Additional slides

Assumptions and hypotheses

1) error stats are normal (or log normal) 2) obs error uncorrelated with background

error 3) obs error not correlated in time 4) best linear unbiased estimator (BLUE)

5) correlation homogeneous and isotropic

BLUE:-No biases in obs/background -Each error is uncorrelated with the state vector-Assumes linearity

Basic equations

K = (HPf)t * (H(HPf)t+R)-1   1) Calculate H(HPf(k1,k2))t = α*σf(k1)*σf(k2)*exp { - |

x(k1)- x(k2)|/(βLc } until χ2/NS = 1 (tuning on the fly)

2) Calculate (HPf(i,j,k1))t = α*σf(i,j)*σf(k1)*exp { - |x(i,j)- x(k1)|/(βLc }

N ~ < 1500

Hypothesis: σf(i,j) and Lc are constant over the whole domainHowever, a sensitivity analysis was done: it turns out that those 2 parameters are quite sensitive and can be tuned to achieved a better optimization.

A

A: positive definite (trace (A) > 0; det |A| > 0)

Note: X2 = ע*A-1*עt

Cross validation OmP (warm/cold season)

Ozone ERN NA Ozone WRN NA

-4

-2

0

2

4

6

8

10

12

14

16

18

1 2 3 4

Series1

Series2

-2

0

2

4

6

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10

12

14

16

18

1 2 3 4

Series1

Series2

-2

0

2

4

6

8

10

12

14

1 2 3 4

Série1

Série2

-2

0

2

4

6

8

10

12

14

16

1 2 3 4

Series1

Series2

Warmseason

Coldseason

Mean

Mean

Meanσ

Meanσ

Meanσ

Meanσ

ppbv

ppbv

ppbv

ppbv

1: Model, 2: OA, 3 et 4 OA with adaptative schemeN~3M (10%)

2006

N~1M (10%)

CHRONOS

Decrease weight ?of obs

Decrease weight ?Of obs

OmA < OmP

OmP < OmA OmP < OmA

OmA < OmP

PM2.5

IncreaseWeight of obs ?

IncreaseWeight of obs

A posteriori tuning

Decrease weight of obs

Std (OmA) >Std (OmP)

2:1 1:1

PM2.5

Increase weightof obs

A posteriori tuning

OA system for surface pollutants

Compatible with EnKF Demonstrated positive impact on model

forecast GEM-MACH and CHRONOS OA system useful for derived products

(AQHI), monitoring of oils sands, climatology, nowcasting and others